In the following items determine whether the proposed negation is correct. If is is not, write a correct negation. (a) Statement: The product of any irrational number and any rational number is irrational. Proposed negation: The product of any irrational number and any rational number is rational. (b) Statement: For all real numbers ₁ and 2, if x² = then ₁ = 1₂. Proposed negation: For all real numbers ₁ and 2, if I1 / 12. then
In the following items determine whether the proposed negation is correct. If is is not, write a correct negation. (a) Statement: The product of any irrational number and any rational number is irrational. Proposed negation: The product of any irrational number and any rational number is rational. (b) Statement: For all real numbers ₁ and 2, if x² = then ₁ = 1₂. Proposed negation: For all real numbers ₁ and 2, if I1 / 12. then
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 20E: Give counterexamples for the following statements.
If and are irrational, then is irrational.
If ...
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